WASHINGTON (CNN) -- A liberal advocacy group's print ad attacking Gen. David Petraeus drew a firestorm of criticism from both sides of the aisle on Monday.

The ad, running in Monday's edition of the New York Times, shows a picture of Petraeus. Bold letters spell out "General Petraeus or General Betray us?"

Moveon.org Political Action, which paid for the ad, accuses Petraeus of "cooking the books for the White House" on progress being made in Iraq and calls him "a military man constantly at war with the facts."

White House spokesman Tony Snow called the ad, running the same day the general testified before Congress about Iraq, a "boorish, childish, unworthy attack."

When asked early Monday if this was the right message for his party to send, the Nevada Democrat curtly answered, "No."

In a separate conversation, a senior Democratic leadership aide called the ad an "unnecessary distraction" and said Democrats are prepared to focus on "Petraeus executing a mismanaged mission."

Reid's decision to distance himself from the ad came as several Republican leaders called on Democrats to condemn it.

"Democratic leaders must make a choice today: Either embrace the character assassination tactics Moveon.org has leveled against the four-star general leading our troops in the fight against al Qaeda, or denounce it as disgraceful," House Minority Leader John Boehner, R-Ohio, said in a statement.

"General Petraeus and the other commanders in the U.S. Armed Services have dedicated their lives to defending the very freedom that enables Moveon.org the right to free speech. I support that right, but I find the way they have chosen to exercise it today to be disrespectful and downright reprehensible," Boehner said.

Sen. Joe Lieberman, D-Connecticut, also called on the Democratic leadership to "denounce Moveon.org attack on Gen. Petraeus." Lieberman has been supportive of President Bush's efforts in Iraq.

Sen. John Kerry, D-Massachusetts, called the ad "over the top."

"I don't like any kind of characterizations in our politics that call into question any active duty, distinguished general who I think under any circumstances serves with the best interests of our country," said Kerry, the 2004 Democratic presidential candidate and a decorated veteran.

"I think there are a lot of legitimate questions that need to be asked, a lot of probing that ought to take place; there's a lot of legitimate accountability that needs to be achieved. It ought to be done without casting any aspersions on anyone's character or motives," he added.

Moveon.org said Monday it stood by the ad completely.

"Every major independent study and many major news organizations cast serious doubt on Petraeus' claims," Eli Pariser, executive director of MoveOn.org Political Action Committee, said in a statement.

"It should come as no surprise that General Petraeus' claims have come under critical scrutiny: The facts all point in one direction -- the surge isn't working -- and General Petraeus and the White House are pointing in another," the statement said.

"No wonder recent polls show that the American people agree with the ad also: A majority expect that the general will deliver 'a biased report that reflects what the Bush administration wants the public to believe,'" the statement said, quoting from a USA Today/Gallup poll reported in Monday's USA Today.